Question

(x-8)(x-k) = x^2 - 5kx +m In the equation above, k and m are constants. If the equation is true for all values of x, what is the value of m?

Answer 1

First expand out (x-8)(x-k) to get


(x-8)(x-k) = x^2 - 5kx + m

x^2 - xk - 8x + 8k = x^2 - 5kx + m

x^2 - (k + 8)x + 8k = x^2 - 5kx + m


Now equate the x terms and solve for k


-(k+8)x = -5kx

-(k+8) = -5k

-k-8 = -5k

-8 = -5k+k

-8 = -4k

-4k = -8

k = -8/(-4)

k = 2


Then use this to find m


8k = m

8*2 = m

16 = m

m = 16


So the original equation turns into


(x-8)(x-k) = x^2 - 5kx + m

(x-8)(x-2) = x^2 - 5*2*x + 16

(x-8)(x-2) = x^2 - 10x + 16

Answer 2

Alright, I almost understand this. My issue comes with "equating the x terms."

I'm at this point: -x(k + 8) +8k = -5kx + m
How can I just say that -x(k + 8) = -5kx ?
And the same with 8k = m ?

I'm sure there is a reasonable explanation; but I just don't see it yet.

Answer 3

the +m is not part of the x terms

Answer 4

the +m is the constant and that is equal to 8k on the left side

Answer 5

So just because it's constant it's equal to the left side?